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A $2.28$-competitive algorithm for online scheduling on identical machines
Sensor deployment for pipeline leakage detection via optimal boundary control strategies
1. | State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems & Control, Zhejiang University, Hangzhou, Zhejiang 310027, China, China, China |
2. | Institute of Operations Research & Cybernetics, Zhejiang University, Hangzhou, Zhejiang 310027, China |
3. | Ningbo Institute of Technology, Zhejiang University, Hangzhou, Zhejiang 310027, China |
References:
[1] |
N. Ahmed and K. Teo, Optimal Control of Distributed Parameter Systems,, North Holland, (1981).
|
[2] |
S. Anita, V. Arnautu and V. Capasso, An Introduction to Optimal Control Problems in Life Sciences and Economics,, Modeling and Simulation in Science, (2011).
doi: 10.1007/978-0-8176-8098-5. |
[3] |
V. Arnautu and P. Neittaanmaki, Optimal Control from Theory to Computer Programs,, Kluwer Academic, (2003).
doi: 10.1007/978-94-017-2488-3. |
[4] |
P. Barooah, P. Mehta and J. Hespanha, Mistuning-based control design to improve closed-loop stability margin of vehicular platoons,, IEEE Transactions on Automatic Control, 54 (2009), 2100.
doi: 10.1109/TAC.2009.2026934. |
[5] |
S. Blazic, D. Matko and G. Geiger, Simple model of a multi-batch driven pipeline,, Mathematics and Computers in Simulation, 64 (2004), 617.
doi: 10.1016/j.matcom.2003.11.013. |
[6] |
F. Bullo, J. Cortes and S. Martinez, Distributed Control of Robotic Networks (In Applied Mathematics Series),, Princeton University Press, (2009).
|
[7] |
M. Chen and D. Georges, Nonlinear optimal control of an open-channel hydraulic system based on an infinite-dimensional model,, in Proceeding of the Conference on Decision and Control, (1999). Google Scholar |
[8] |
H. Cho and G. Hwang, Optimal design for dynamic spectrum access in cognitive radio networks under rayleigh fading,, Journal of Industrial and Management Optimization, 8 (2012), 821.
doi: 10.3934/jimo.2012.8.821. |
[9] |
E. Chow, L. Hendrix, M. Herberg, S. Itoh, B. Kong, M. Lall and P. Srevens, Pipeline Politics in Asia: The Intersection of Demand, Energy Markets, and Supply Routes,, National Bureau of Asian Research, (2010). Google Scholar |
[10] |
Y. Ding and S. Wang, Optimal control of open-channel flow using adjoint sensitivity analysis,, Journal of Hydraulic Engineering-ASCE, 132 (2006), 1215.
doi: 10.1061/(ASCE)0733-9429(2006)132:11(1215). |
[11] |
Z. Feng, K. Teo and V. Rehbock, Branch and bound method for sensor scheduling in discrete time,, Journal of Industrial and Management Optimization, 1 (2005), 499.
doi: 10.3934/jimo.2005.1.499. |
[12] |
Z. Feng, K. Teo and V. Rehbock, Hybrid method for a general optimal sensor scheduling problem in discrete time,, Automatica, 44 (2008), 1295.
doi: 10.1016/j.automatica.2007.09.024. |
[13] |
G. Ferrari-Trecate, A. Buffa and M. Gati, Analysis of coordination in multi-agent systems through partial difference equations,, IEEE Transactions on Automatic Control, 51 (2006), 1058.
doi: 10.1109/TAC.2006.876805. |
[14] |
P. Frihauf and M. Krstic, Leader-enabled deployment onto planar curves: A pde-based approach,, IEEE Transactions on Automatic Control, 56 (2011), 1791.
doi: 10.1109/TAC.2010.2092210. |
[15] |
R. Glowinski, J. Lions and J. He, Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach,, (Encyclopedia of Mathematics and its Applications) Cambridge University Press, (2008).
doi: 10.1017/CBO9780511721595. |
[16] |
H. Hao and P. Barooah, On achieving size-independent stability margin of vehicular lattice formations with distributed control,, IEEE Transactions on Automatic Control, 57 (2012), 2688.
doi: 10.1109/TAC.2012.2191179. |
[17] |
H. Hao, P. Barooah and P. Mehta, Stability margin scaling laws for distributed formation control as a function of network structure,, IEEE Transactions on Automatic Control, 56 (2011), 923.
doi: 10.1109/TAC.2010.2103416. |
[18] |
J. Kim, K. Kim, V. Natarajan, S. Kelly and J. Bentsman, PdE-based model reference adaptive control of uncertain heterogeneous multiagent networks,, Nonlinear Analysis: Hybrid Systems, 2 (2008), 1152.
doi: 10.1016/j.nahs.2008.09.008. |
[19] |
J. Kim, V. Natarajan, S. Kelly and J. Bentsman, Disturbance rejection in robust PdE-based MRAC laws for uncertain heterogeneous multiagent networks under boundary reference,, Nonlinear Analysis: Hybrid Systems, 4 (2010), 484.
doi: 10.1016/j.nahs.2009.11.005. |
[20] |
M. Krstic and A. Smyshlyaev, Boundary Control of PDEs: A Course on Backstepping Designs,, SIAM, (2008).
doi: 10.1137/1.9780898718607. |
[21] |
Z. Lin, Distributed Control and Analysis of Coupled Cell Systems,, VDM Verlag, (2008). Google Scholar |
[22] |
W. Litvinov, Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions,, Journal of Industrial and Management Optimization, 7 (2011), 291.
doi: 10.3934/jimo.2011.7.291. |
[23] |
M. Liu, S. Zang and D. Zhou, Fast leak detection and location of gas pipelines based on an adaptive particle filter,, International Journal of Applied Mathematics and Computer Science, 15 (). Google Scholar |
[24] |
M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multiagent Networks (In Applied Mathematics Series),, Princeton University Press, (2010).
|
[25] |
T. Meurer and M. Krstic, Finite-time multi-agent deployment: A nonlinear pde motion planning approach,, Automatica, 47 (2011), 2534.
doi: 10.1016/j.automatica.2011.08.045. |
[26] |
S. Moura and H. Fathy, Optimal boundary control & estimation of diffusion-reaction PDEs,, in Proceeding of the Conference on Decision and Control, (2011), 921. Google Scholar |
[27] |
R. Murray, Recent research in cooperative control of multi-vehicle systems,, Journal of Dynamical Systems, (): 571. Google Scholar |
[28] |
R. Olfati-Saber and R. Murray, Consensus problems in networks of agents with switching topology and time-delays,, IEEE Transactions on Automatic Control, 49 (2004), 1520.
doi: 10.1109/TAC.2004.834113. |
[29] |
P. Parfomak, Pipeline Safety and Security: Federal Programs,, Congress Research Services (CRS) Report for Congress, (2008). Google Scholar |
[30] |
M. Rafiee, Q. Wu and A. Bayen, Kalman filter based estimation of flow states in open channels using Lagrangian sensing,, Proceedings of the Conference on Decision and Control, (2009), 8266.
doi: 10.1109/CDC.2009.5400661. |
[31] |
W. Ren and Y. Cao, Distributed Coordination of Multi-agent Networks,, (Communications and Control Engineering Series) Springer-Verlag, (2011). Google Scholar |
[32] |
A. Sarlette and R. Sepulchre, A PDE viewpoint on basic properties of coordination algorithms with symmetries,, in Proceedings of the Conference on Decision and Control, (2009), 5139.
doi: 10.1109/CDC.2009.5400570. |
[33] |
J. Strikwerda, Finite Difference Schemes and Partial Differential Equations, 2nd Edition,, SIAM, (2004).
doi: 10.1137/1.9780898717938. |
[34] |
F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods and Applications (Graduate Studies in Mathematics),, American Mathematical Society, (2010).
|
[35] |
G. Wang and H. Ye, Leakage Detection and Localization of Long Distance Fluid Pipelines,, Tsinghua University Press, (2010). Google Scholar |
[36] |
Z. Wang, H. Zhang, J. Feng and S. Lun, Present situation and prospect on leak detection and localization techniques for long distance fluid transport pipeline,, Control and Instruments in Chemical Industry, 30 (2003), 5. Google Scholar |
[37] |
S. Woon, V. Rehbock and R. Loxton, Global optimization method for continuous-time sensor scheduling,, Nonlinear Dynamics and Systems Theory, 10 (2010), 175.
|
[38] |
S. Woon, V. Rehbock and R. Loxton, Towards global solutions of optimal discrete-valued control problems,, Optimal Control Applications and Methods, 33 (2012), 576.
doi: 10.1002/oca.1015. |
[39] |
K. Yiu, K. Mak and K. Teo, Airfoil design via optimal control theory,, Journal of Industrial and Management Optimization, 1 (2005), 133.
doi: 10.3934/jimo.2005.1.133. |
[40] |
C. Yu, B. Li, R. Loxton and K. Teo, Optimal discrete-valued control computation,, Journal of Global Optimization, 56 (2013), 503.
doi: 10.1007/s10898-012-9858-7. |
show all references
References:
[1] |
N. Ahmed and K. Teo, Optimal Control of Distributed Parameter Systems,, North Holland, (1981).
|
[2] |
S. Anita, V. Arnautu and V. Capasso, An Introduction to Optimal Control Problems in Life Sciences and Economics,, Modeling and Simulation in Science, (2011).
doi: 10.1007/978-0-8176-8098-5. |
[3] |
V. Arnautu and P. Neittaanmaki, Optimal Control from Theory to Computer Programs,, Kluwer Academic, (2003).
doi: 10.1007/978-94-017-2488-3. |
[4] |
P. Barooah, P. Mehta and J. Hespanha, Mistuning-based control design to improve closed-loop stability margin of vehicular platoons,, IEEE Transactions on Automatic Control, 54 (2009), 2100.
doi: 10.1109/TAC.2009.2026934. |
[5] |
S. Blazic, D. Matko and G. Geiger, Simple model of a multi-batch driven pipeline,, Mathematics and Computers in Simulation, 64 (2004), 617.
doi: 10.1016/j.matcom.2003.11.013. |
[6] |
F. Bullo, J. Cortes and S. Martinez, Distributed Control of Robotic Networks (In Applied Mathematics Series),, Princeton University Press, (2009).
|
[7] |
M. Chen and D. Georges, Nonlinear optimal control of an open-channel hydraulic system based on an infinite-dimensional model,, in Proceeding of the Conference on Decision and Control, (1999). Google Scholar |
[8] |
H. Cho and G. Hwang, Optimal design for dynamic spectrum access in cognitive radio networks under rayleigh fading,, Journal of Industrial and Management Optimization, 8 (2012), 821.
doi: 10.3934/jimo.2012.8.821. |
[9] |
E. Chow, L. Hendrix, M. Herberg, S. Itoh, B. Kong, M. Lall and P. Srevens, Pipeline Politics in Asia: The Intersection of Demand, Energy Markets, and Supply Routes,, National Bureau of Asian Research, (2010). Google Scholar |
[10] |
Y. Ding and S. Wang, Optimal control of open-channel flow using adjoint sensitivity analysis,, Journal of Hydraulic Engineering-ASCE, 132 (2006), 1215.
doi: 10.1061/(ASCE)0733-9429(2006)132:11(1215). |
[11] |
Z. Feng, K. Teo and V. Rehbock, Branch and bound method for sensor scheduling in discrete time,, Journal of Industrial and Management Optimization, 1 (2005), 499.
doi: 10.3934/jimo.2005.1.499. |
[12] |
Z. Feng, K. Teo and V. Rehbock, Hybrid method for a general optimal sensor scheduling problem in discrete time,, Automatica, 44 (2008), 1295.
doi: 10.1016/j.automatica.2007.09.024. |
[13] |
G. Ferrari-Trecate, A. Buffa and M. Gati, Analysis of coordination in multi-agent systems through partial difference equations,, IEEE Transactions on Automatic Control, 51 (2006), 1058.
doi: 10.1109/TAC.2006.876805. |
[14] |
P. Frihauf and M. Krstic, Leader-enabled deployment onto planar curves: A pde-based approach,, IEEE Transactions on Automatic Control, 56 (2011), 1791.
doi: 10.1109/TAC.2010.2092210. |
[15] |
R. Glowinski, J. Lions and J. He, Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach,, (Encyclopedia of Mathematics and its Applications) Cambridge University Press, (2008).
doi: 10.1017/CBO9780511721595. |
[16] |
H. Hao and P. Barooah, On achieving size-independent stability margin of vehicular lattice formations with distributed control,, IEEE Transactions on Automatic Control, 57 (2012), 2688.
doi: 10.1109/TAC.2012.2191179. |
[17] |
H. Hao, P. Barooah and P. Mehta, Stability margin scaling laws for distributed formation control as a function of network structure,, IEEE Transactions on Automatic Control, 56 (2011), 923.
doi: 10.1109/TAC.2010.2103416. |
[18] |
J. Kim, K. Kim, V. Natarajan, S. Kelly and J. Bentsman, PdE-based model reference adaptive control of uncertain heterogeneous multiagent networks,, Nonlinear Analysis: Hybrid Systems, 2 (2008), 1152.
doi: 10.1016/j.nahs.2008.09.008. |
[19] |
J. Kim, V. Natarajan, S. Kelly and J. Bentsman, Disturbance rejection in robust PdE-based MRAC laws for uncertain heterogeneous multiagent networks under boundary reference,, Nonlinear Analysis: Hybrid Systems, 4 (2010), 484.
doi: 10.1016/j.nahs.2009.11.005. |
[20] |
M. Krstic and A. Smyshlyaev, Boundary Control of PDEs: A Course on Backstepping Designs,, SIAM, (2008).
doi: 10.1137/1.9780898718607. |
[21] |
Z. Lin, Distributed Control and Analysis of Coupled Cell Systems,, VDM Verlag, (2008). Google Scholar |
[22] |
W. Litvinov, Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions,, Journal of Industrial and Management Optimization, 7 (2011), 291.
doi: 10.3934/jimo.2011.7.291. |
[23] |
M. Liu, S. Zang and D. Zhou, Fast leak detection and location of gas pipelines based on an adaptive particle filter,, International Journal of Applied Mathematics and Computer Science, 15 (). Google Scholar |
[24] |
M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multiagent Networks (In Applied Mathematics Series),, Princeton University Press, (2010).
|
[25] |
T. Meurer and M. Krstic, Finite-time multi-agent deployment: A nonlinear pde motion planning approach,, Automatica, 47 (2011), 2534.
doi: 10.1016/j.automatica.2011.08.045. |
[26] |
S. Moura and H. Fathy, Optimal boundary control & estimation of diffusion-reaction PDEs,, in Proceeding of the Conference on Decision and Control, (2011), 921. Google Scholar |
[27] |
R. Murray, Recent research in cooperative control of multi-vehicle systems,, Journal of Dynamical Systems, (): 571. Google Scholar |
[28] |
R. Olfati-Saber and R. Murray, Consensus problems in networks of agents with switching topology and time-delays,, IEEE Transactions on Automatic Control, 49 (2004), 1520.
doi: 10.1109/TAC.2004.834113. |
[29] |
P. Parfomak, Pipeline Safety and Security: Federal Programs,, Congress Research Services (CRS) Report for Congress, (2008). Google Scholar |
[30] |
M. Rafiee, Q. Wu and A. Bayen, Kalman filter based estimation of flow states in open channels using Lagrangian sensing,, Proceedings of the Conference on Decision and Control, (2009), 8266.
doi: 10.1109/CDC.2009.5400661. |
[31] |
W. Ren and Y. Cao, Distributed Coordination of Multi-agent Networks,, (Communications and Control Engineering Series) Springer-Verlag, (2011). Google Scholar |
[32] |
A. Sarlette and R. Sepulchre, A PDE viewpoint on basic properties of coordination algorithms with symmetries,, in Proceedings of the Conference on Decision and Control, (2009), 5139.
doi: 10.1109/CDC.2009.5400570. |
[33] |
J. Strikwerda, Finite Difference Schemes and Partial Differential Equations, 2nd Edition,, SIAM, (2004).
doi: 10.1137/1.9780898717938. |
[34] |
F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods and Applications (Graduate Studies in Mathematics),, American Mathematical Society, (2010).
|
[35] |
G. Wang and H. Ye, Leakage Detection and Localization of Long Distance Fluid Pipelines,, Tsinghua University Press, (2010). Google Scholar |
[36] |
Z. Wang, H. Zhang, J. Feng and S. Lun, Present situation and prospect on leak detection and localization techniques for long distance fluid transport pipeline,, Control and Instruments in Chemical Industry, 30 (2003), 5. Google Scholar |
[37] |
S. Woon, V. Rehbock and R. Loxton, Global optimization method for continuous-time sensor scheduling,, Nonlinear Dynamics and Systems Theory, 10 (2010), 175.
|
[38] |
S. Woon, V. Rehbock and R. Loxton, Towards global solutions of optimal discrete-valued control problems,, Optimal Control Applications and Methods, 33 (2012), 576.
doi: 10.1002/oca.1015. |
[39] |
K. Yiu, K. Mak and K. Teo, Airfoil design via optimal control theory,, Journal of Industrial and Management Optimization, 1 (2005), 133.
doi: 10.3934/jimo.2005.1.133. |
[40] |
C. Yu, B. Li, R. Loxton and K. Teo, Optimal discrete-valued control computation,, Journal of Global Optimization, 56 (2013), 503.
doi: 10.1007/s10898-012-9858-7. |
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